Narrow Results

We show an improvement of Bray sharp mass–capacity inequality and Bray–Miao sharp upper bound of the capacity of the boundary in terms of its area, for three-dimensional, complete, one-ended asymptotically flat manifolds with compact, connected boundary and with nonnegative scalar curvature, under appropriate assumptions on the topology and on the mean curvature of the boundary. Our arguments relies on two monotonicity formulas holding along level sets of a suitable harmonic potential, associated to the boundary of the manifold. This work is an expansion of the results contained in the Ph.D. thesis [F. Oronzio, ADM mass and linear potential theory, Ph.D. thesis, Università degli studi di Napoli Federico II (2022)] of the author.

In this paper, we establish the existence of a renormalized solution to the initial-boundary problem to the parabolic differential problem involving variable exponent under the Leray–Lions type of conditions. We show the independence of the definition of the renormalized solution of the decomposition of the given measure, and applying the approximation approach we establish the existence of a renormalized solution to the parabolic problem with measure data, which does not charge the sets of zero capacity.

The paper reviews some parts of classical potential theory with applications to two-dimensional fluid dynamics, in particular vortex motion. Energy and forces within a system of point vortices are similar to those for point charges when the vortices are kept fixed, but the dynamics is different in the case of free vortices. Starting from Euler’s and Bernoulli’s equations we derive these laws. Letting the number of vortices tend to infinity leads in the limit to considerations of equilibrium distributions, capacity, harmonic measure and many other notions in potential theory. In particular various kinds of Green functions have a central role in the paper, and we make a distinction between electrostatic and hydrodynamic Green functions. We also consider the corresponding concepts in the case of closed Riemann surfaces provided with a metric. From a canonically defined monopole Green function we rederive much of the classical theory of harmonic and analytic forms on Riemann surfaces. In the final section of the paper we return to the planar case, which then reappears in the form of a symmetric Riemann surface, the Schottky double. Bergman kernels, electrostatic and hydrodynamic, come up naturally as well as other kernels, and associated to the Green function there is a certain Robin function which is important for vortex motion, and which also relates to capacity functions in classical potential theory.

To explore the influence of chunking on the capacity limits of working memory, a model for chunking in sequential working memory is proposed, using hierarchical bidirectional inhibition-connected neural networks with winnerless competition. With the assumption of the existence of an upper bound to the inhibitory weights in neurobiological networks, it is shown that chunking increases the number of memorized items in working memory from the "magical number 7" to 16 items. The optimal number of chunks and the number of the memorized items in each chunk are the "magical number 4".

We will study certain boundary measures related to $m$-subharmonic functions on $m$-hyperconvex domains. These measures generalize the boundary measures studied by Wan and Wang (see [Complex Hessian operator and Lelong number for unbounded $m$-subharmonic functions, Potential. Anal.44(1) (2016) 53–69]). For the case of plurisubharmonic functions ($m=n$) the boundary measure has been studied by Cegrell and Kemppe (see [Monge–Ampère boundary measures, Ann. Polon. Math.96 (2009) 175–196]).

We prove that every locally pluripolar set on a compact complex manifold is pluripolar. This extends similar results in the Kähler case.

Let $\phi$ be a function in the complex Sobolev space $W^{\ast }(U)$, where $U$ is an open subset in ${ℂ}^k$. We show that the complement of the set of Lebesgue points of $\phi$ is pluripolar. The key ingredient in our approach is to show that $|\phi {|}^{\alpha }$ for $\alpha \in [1,2)$ is locally bounded from above by a plurisubharmonic function.

In this paper, we investigate the lane expansion effect of the tollbooth system. To this end, two typical values of randomization probability p:p=0.5 and p=0.1 are chosen. It is shown that for p=0.5, the full capacity of the single lane highway can be restored. However, for p=0.1, our simulations show that the full capacity of the single lane highway cannot be restored due to the existence of the merge section in the lane expansion section. Moreover, we have investigated the dependence of road capacity on the length of lane expansion section as well as the effects of the positions of the tollbooths in the lane expansion section under different values of p.

Understanding the hydrogen (H) capacity, which represents the tritium capacity in Li₂TiO₃ crystal has become an important aspect of the tritium release process of nuclear fusion. In this work, a systematic density-functional-theory (DFT) study is performed to investigate the trapping and accumulation of H in Li₂TiO₃ crystal. In perfect crystal, the H adsorption properties are investigated and the maximum number of trapped H atoms are obtained. In the defect models, by calculating the trapping energy and Bader charge, we find that a Li vacancy can capture four H atoms while the capacity of a Ti vacancy is seven and then other H atoms tend to be trapped by interstitial sites outside the vacancy. Then the H capacity both inside and outside the vacancy in the defect models is studied and analyzed. According to our calculations, crystals containing a vacancy present stronger H trapping abilities than perfect crystals, especially for the crystal with a Ti vacancy. In addition, the increase of H atoms in the vacancy facilitates the formation of the neighboring vacancy so that more H atoms can be accommodated in the crystal with vacancy. Our results reveal the H capacity of different Li₂TiO₃ models, which provide theoretical support for related tritium release experiments.

In response to urban rail transit capacity shortage, a capacity adaption optimization model for the new mixed train operation mode is proposed in the supernormal operation of urban rail transit networks. First, the characteristics of express-local train and long-short route slow train are analyzed to obtain the main influencing factors of capacity adaption. Moreover, various train types are simultaneously classified and recombined in the adaption train operation mode to maximize transportation capacity for passengers. A nonlinear mixed-integer programming model is established to maximize the total number of trains, improving train load rate and reducing the total passenger travel time. In addition, the actual case of Beijing Metro Line 1 is solved to demonstrate the feasibility and effectiveness of the proposed model. The optimal passenger travel time-saving rates of the morning and evening peak hours are 12.1% and 11.5%, respectively. The optimal utilization rates of capacity in the morning and evening peak hours are 79.5% and 84.5%, respectively. Meanwhile, the optimal load factor within the range of 0.7–0.9 would benefit the utilization of train resources and the passengers’ service level. The optimized results show that the proposed capacity adaption optimization model benefits for high service level and practical significance and rationality for operators.

Much research attention has been devoted to the investigation of how the structure of a network affects its intended performance. However, conclusions drawn from the previous studies are often inconsistent and even contradictory. In order to identify the causes of these diverse results and to explore the impact of network topology on performance, we apply the concept of bifurcation in dynamical systems and consider the effect of varying a crucial parameter for networks of different structures. In this paper, we study transmission networks and identify the capacity setting as the parameter. Upon varying this parameter, the behavioral change of the network is observed. Specifically, we focus on communication networks and power grids, and study the improvement or degradation of robustness of such networks under variation of link capacity. We observe that the effect of increasing link capacity on robustness differs for different networks, and a bifurcation point exists in some cases which divides regions of opposite robustness behavior. Our work demonstrates that capacity settings play a crucially important role in determining how network structure affects the intended performance of transmission networks, and clarifies the previous reported contradictory results.

We establish new lower semicontinuity results for energy functionals containing a very general volume term of polyconvex type and a surface term depending on the spatial variable in a discontinuous way.

We provide a survey of recent developments about capacities (or fuzzy measures) and cooperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of usual tools in these theories, such as the Choquet integral, the Möbius transform, and the Shapley value.

The aim of this paper is to propose a new measure approach of ambiguous risk aversion under some capacity μ (a non-additive measure), in particular, under the distorted probability. Firstly, by using the Choquet integral with respect to the capacity μ, we introduce the concept of ambiguous risk premium of a risk asset X for risk aversive individuals whose utility function is u, and we investigate some properties of the ambiguous risk premium under some assumptions. Then to illustrate our theoretical results, we give an example and empirical results.

Generalizing a first approach by L. A. ZADEH (J. Math. Anal. Appl. 23, 1968), expected values of fuzzy events are studied which are (up to standard boundary conditions) only required to be monotone. They can be seen as an extension of capacities, i.e., monotone set functions satisfying standard boundary conditions. Some of these expected values can be characterized axiomatically, others are based on some distinguished integrals (Choquet, Sugeno, Shilkret, universal, and decomposition integral).

Bi-Choquet Integrals based on bi-capacities are very powerful aggregation operators introduced by Grabisch and Labreuche, and they can generalize Choquet Integrals. Bi-capacities can model a lager range of preferences than capacities. However, there are few existent knowledge about constructing bi-capacities, and there lacks the practical and reasonable orness/andness definitions for bi-capacities to present an effective optimism/pessimism indicator. We present a convenient way to generate bi-capacities. As the main proposal of this study, we propose an orness/andness definition for bi-capacities. Although structurally complex in defining, with the help of one interesting proposition related to bi-Choquet Integral, its reasonability in the way of constructing further proves it can indeed serve as a perfect generalization of orness/andness for capacities.

The solution of Meyerowitz, Richman and Walker to the problem of determining the maximum-entropy probability consistent with a belief function (an ∞-monotone capacity) is shown to remain valid in the case of a convex (i.e., 2-monotone) capacity.

This article is mainly to study the reliability evaluation in terms of MPs (minimal paths) for a multistate flow network G in which the capacities of each arc are real numbers. The transportation system from the source node s to the sink node t is one of such typical networks. Given the system demand d from s to t and MPs in advance, an algorithm is proposed first to find out all lower boundary points of level d (namely d-MPs here). The system reliability which is the probability that the system flow satisfies the demand d can be calculated in terms of such d-MPs. One example is presented to illustrate how all its d-MPs are generated. The computational time complexity in the worst case and average cases for such an algorithm is presented.

Three different electrode films of highly crystallized LiCoO₂, nano-crystalline LiMn₂O₄ as cathode and amorphous LiNiVO₄ as anode were grown on stainless steel substrates by pulsed laser deposition. Microbatteries were assembled using liquid electrode of LiPF₆. The microbatteries were electrochemically tested by charge/discharge cycling and cyclic voltammetry. Both LiCoO₂/LiPF₆/LiNiVO₄ and LiMn₂O₄/LiPF₆/LiNiVO₄ cells showed smooth charge/discharge curves. Although the cells faced a fast capacity loss in the first 10 cycles, about 20 μA/cm² μm of discharge capacity was attainable after 20 cycles.

We distinguish three classes of capacities on a C*-algebra: subadditive, additive and maxitive. A tightness notion for capacities, the vague and narrow topologies on the set of capacities are introduced. The vague space of additive capacities which are finite on compact projections is a noncommutative version of the usual vague space of Radon measures on a locally compact Hausdorff space X. We give criterions of vague and narrow relative compactness in various classes of capacities. This allows us to extend most classical compactness theorems for Radon measures. The set of bounded (resp. tight) maxitive capacities is in bijection with the set of positive q-upper semicontinuous (resp. strongly q-upper semicontinuous) operators. This allows us to define a vague (resp. narrow) large deviation principle for a net of capacities as a vague (resp. narrow) convergence of this net towards a maxitive capacity, generalizing the classical notion for Radon probability measures on X. Next, we apply compactness theorems in order to extend some results in large deviations theory.